Show `f(x) = (1)/(|x|)` has discontinuity of second kind at x = 0.

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

Function f(x)=x-|x| is discontinuous at x=0

Show that f(x) = x-[x] is discontinuous for integral values of x

Show that f(x)={1+x^(2),quad if quad 0 is discontinuous at x=1

Let f(x) =x[1/x]+x[x] if x!=0 ; 0 if x =0 where[x] denotes the greatest integer function. then the correct statements are (A) Limit exists for x=-1 (B) f(x) has removable discontinuity at x =1 (C) f(x) has non removable discontinuity at x =2 (D) f(x) is non removable discontinuous at all positive integers

Match the following for the type of discontinuity at x=1 in column II for the function in column I. f(x)=1/(x-1) , p. Removable discontinuity f(x)=(x^3-x)/(x^2-1) , q. Non-removable discontinuity f(x)=(|x-1|)/(x-1) , r. Jump of discontinuity f(x)=sin(1/(x-1)) , s. Discontinuity due to vertical asymptote , t. Missing point discontinuity , u. Oscillating discontinuity

Match the following for the type of discontinuity at x=1 in column II for the function in column I. f(x)=1/(x-1) , p. Removable discontinuity f(x)=(x^3-x)/(x^2-1) , q. Non-removable discontinuity f(x)=(|x-1|)/(x-1) , r. Jump of discontinuity f(x)=sin(1/(x-1)) , s. Discontinuity due to vertical asymptote , t. Missing point discontinuity , u. Oscillating discontinuity

Match the following for the type of discontinuity at x=1 in column II for the function in column I. f(x)=1/(x-1) , p. Removable discontinuity f(x)=(x^3-x)/(x^2-1) , q. Non-removable discontinuity f(x)=(|x-1|)/(x-1) , r. Jump of discontinuity f(x)=sin(1/(x-1)) , s. Discontinuity due to vertical asymptote , t. Missing point discontinuity , u. Oscillating discontinuity

Match the following for the type of discontinuity at x=1 in column II for the function in column I. f(x)=1/(x-1) , p. Removable discontinuity f(x)=(x^3-x)/(x^2-1) , q. Non-removable discontinuity f(x)=(|x-1|)/(x-1) , r. Jump of discontinuity f(x)=sin(1/(x-1)) , s. Discontinuity due to vertical asymptote , t. Missing point discontinuity , u. Oscillating discontinuity

Consider the function defined on [0,1] -> R, f(x) = (sinx - x cosx)/x^2 and f(0) = 0, then the function f(x)-(A) has a removable discontinuity at x = 0(B) has a non removable finite discontinuity at x = 0(C) has a non removable infinite discontinuity at x = 0(D) is continuous at x = 0